x''(t)-4x(t)=2. First find the homogeneous x''(t)-4x(t)=0, characteristic equation m^2-4=0, m1/2=+-2, xh=C1*e^(m1*t)+C2*e^(m2*t)=C1e^(2*t)+C2*e^(-2*t). As we see that a non homogeneous part in start equation is 2, xp must be constant. x=xh+xp. Substitute this in start equation (C1*e^2t+C2*e(-2t)+xp)''-4(C1*e^2t+C2*e(-2t)+xp)=2, xp''=0, -4xp=2, xp=-1/2.

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